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 Rationalizing Decimals (Posted on 2007-09-26)
Consider the rational number which in decimal form is .12345345345345...
It begins with two non-repeating digits followed by a block of 3 digits which repeats.

For the generalized repeating decimal .[a][b][b][b][b]...
Where [a] has n digits and [b] has m digits.

Find a general way to transform it into a rational number of the form p/r.

 Submitted by Jer Rating: 3.0000 (2 votes) Solution: (Hide) The formula would be ([a]*10^m + [b] - [a])/((10^m - 1)(10^n)) Which is equavalent to the following: The numerator is the number [a][b] - [a] and the denominator is the number consisting of m 9's followed by n 0's. The number in the example is (12345-12)/99900 = 12333/99900 = 4111/33300

Comments: ( You must be logged in to post comments.)
 Subject Author Date re: A little mistake K Sengupta 2007-09-28 07:28:07 A little mistake Chesca Ciprian 2007-09-27 15:50:43 Answer K Sengupta 2007-09-27 06:04:11 Short Old Original Oskar! 2007-09-26 13:26:51 Solution Bractals 2007-09-26 12:52:24 re: How about the numerator? Charlie 2007-09-26 12:11:15 How about the numerator? Jer 2007-09-26 11:05:27 solution Charlie 2007-09-26 10:37:45

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